In a letter to the Australian radio station 2day FM’s parent company, the hospital’s chairman Lord Glenarthur said he wanted to “protest” against the “extremely foolish” gag which he branded “truly appalling”.

His comments follow the apparent suicide on Friday of nurse Jacintha Saldanha, 46, who was on duty at the hospital when she was duped by DJs Mel Greig and Michael Christian into helping reveal details about the Duchess of Cambridge’s health.

Lord Glenarthur said her death was “tragic beyond words”.

His letter to Southern Cross Austereo said the immediate consequence of the station’s “premeditated and ill-considered actions” led to the “humiliation” of Ms Saldanha and another nurse.

“I appreciate that you cannot undo the damage which has been done but I would urge you to take steps to ensure that such an incident could never be repeated,” it added.

A spokesman for the private London hospital, where the pregnant Duchess had been treated for a severe form of morning sickness, said the letter was sent earlier today.

Ms Saldanha was pronounced dead at staff accommodation close to the hospital.

She answered the presenters’ call and, believing they were members of the Royal Family, put them through to another nurse who described Kate’s condition in detail.

The nurse’s devastated family were being comforted by relatives and friends at their terrace home at Greystoke Avenue, Southmead, Bristol.

A friend at the address said Ms Saldanha’s partner Benedict Barboza, 49, and their teenage son and daughter, aged 14 and 16, were “very, very shocked and unhappy at the tragedy”.

News of her death led to a huge backlash against the two presenters, Greig and Christian, who broadcast the prank on their Hot30 Countdown show on 2day FM.

They have now been taken off the air while the Sydney-based station has been inundated with complaints.

But Southern Cross Austereo chief executive Rhys Holleran stood by the two DJs and said they were shocked and devastated by news of Ms Saldanha’s death.

At a news conference in Melbourne, he said: “This is a tragic event that could not have been reasonably foreseen and we’re deeply saddened by it.

“I spoke to both presenters early this morning and it’s fair to say they’re completely shattered.”

Greig and Christian, who put on fake English accents and pretended to be the Queen and Prince of Wales, made an initial apology but continued to boast about the stunt, describing it as the “easiest prank call ever made”.

A flood of complaints have been made to the Australian Communications and Media Authority, which regulates radio broadcasting. It said it is currently in discussions with the station over the matter.

In a statement last night, Ms Saldanha’s family said they were “deeply saddened” by the death and asked for privacy.

They said: “We as a family are deeply saddened by the loss of our beloved Jacintha. We would ask that the media respect our privacy at this difficult time.”

The Duke and Duchess of Cambridge have sent their condolences to Ms Saldanha’s family.

In a statement on Friday night, St James’s Palace said: “The Duke and Duchess of Cambridge are deeply saddened to learn of the death of Jacintha Saldanha.

“Their Royal Highnesses were looked after so wonderfully well at all times by everybody at King Edward VII’s Hospital, and their thoughts and prayers are with Jacintha Saldanha’s family, friends and colleagues at this very sad time.”

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